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When we combine the two statements, here's an efficient way to determine whether we have sufficient information to determine the value of x:
1. Plug in values for the angle measurements, satisfying the constraints in the problem and the rules of geometry.
2. Determine the value of x.
3. Plug in a different set of values, again satisfying the constraints in the problem and the rules of geometry.
4. Determine the value of x.
If the value of x is the same in each case, the two statements combined are SUFFICIENT.
If the value of x changes, the two statements combined are INSUFFICIENT.
Below are two sets of angle measurements that satisfy the rules of geometry and the constraints in the two statements:
∠PRT + ∠PTR = 90 because triangle PRT is a right triangle.
Since QR=RS, ∠RQS = ∠RSQ.
Since ST=TU, ∠UST = ∠SUT.
Since the sum of angles that form a straight line is 180, x = 180 - ∠RQS - ∠UST.
In each case, x=45.
Thus, the two statements combined are SUFFICIENT to determine the value of x.
The correct answer is C.
